Method to solve Simultaneous Equations with two or more than two variables

Method 

Above we have seen equations wherein we are required to find the value of the variable x only. Apart from the equations of the type we have seen above, simple equations of the form 7x + 2y = 47 also exists. As against the equations x - 3 = 12 or 3x + 5 = 20 where we had a single variable x, we have two variables x and y. If we express this equation in terms of y it will be

                   7x + 2y                = 47

                   7x - 7x + 2y          = 47 - 7x

                   0 + 2y                  = 47 - 7x

                    2y                      = 47 - 7x

               

In this expression by giving values to x and solving the expression we get corresponding values for y.

Now if another equation of the form 5x - 4y = 1 is expressed in terms of y, we have

y

=

For this equation also if we substitute values for x, we would get corresponding values for y.

At this stage if we want values which satisfy both the equations then the values of y in both these equations should be identical. That is,

On cross multiplying, we have 4(47 - 7x) = 2(5x - 1)

                   188 - 28x = 10x - 2

Collecting all x terms and constants, we have

                 -10x - 28x    =    - 2 - 188

                         -38x    =    - 190

                              x    =       5

We substitute this value of x = 5, in either of equations to get the value of y.

                   5x - 4y     =     1

                   5(5) - 4y  =     1

                   - 4y         =     1 - 25

                   - 4y         =       - 24

                       y         =       -24/ - 4 = 6.

Therefore, the common values of x and y which satisfy these two equations simultaneously are x = 5 and y = 6. Therefore, we can define simultaneous equations as two or more equations which are satisfied by the same values of x and y (unknown quantities). 

Posted Date: 9/13/2012 3:53:25 AM | Location : United States

Ask an Expert

Related Discussions:- Simultaneous equations with two or more than two variables, Assignment Help, Ask Question on Simultaneous equations with two or more than two variables, Get Answer, Expert's Help, Simultaneous equations with two or more than two variables Discussions

Write discussion on Simultaneous equations with two or more than two variables
Your posts are moderated

Write your message here..

Related Questions

Solve sin (3t ) = 2 trig function, Solve sin (3t ) = 2 . Solution T... Solve sin (3t ) = 2 . Solution This example is designed to remind you of certain properties about sine and cosine.  Recall that -1 ≤ sin (θ ) ≤ 1 and -1 ≤ cos(θ ) ≤ 1 .  Th

Quantitative Techniques, The following table given the these scores and sal... The following table given the these scores and sales be nine salesman during last one year in a certain firm: text scores sales (in 000''rupees) 14 31 19

What is the expected value of perfect information, Question: The follow... Question: The following payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature. (a) Construct a decision tr

Prove that the height of the center of the balloon, A round balloon of radi... A round balloon of radius 'a' subtends an angle θ at the eye of the observer while the angle of elevation of its centre is Φ.Prove that the height of the center of the balloon is a

MATH HELP: URGENT, the andersons are buying a new home and need to fence th... the andersons are buying a new home and need to fence their yard. the yard is 40 ft by 80 ft. each fencing section is 8ft. how many sections will they need?how many posts will they

#rounding off, I am the least two digit number which round off to 100? I am the least two digit number which round off to 100?

#title LOGIC, HOW MANY ZERO ARE THERE AT THE END OF 200 HOW MANY ZERO ARE THERE AT THE END OF 200

Solid mensuration, given dimensions: 130cm, 180cm, and 190cm is to be divid... given dimensions: 130cm, 180cm, and 190cm is to be divided by a line bisecting the longest side shown from its opposite vertex. what''s the area adjacent to 180cm? ;

Vector functions - three dimensional space, Vector Functions We very f... Vector Functions We very firstly saw vector functions back while we were looking at the Equation of Lines. In that section we talked about them as we wrote down the equation o

MATH HONORS, HOW DO YOU DO BAR DIAGRAMS ANDESTIMATE IT WITH PERCENTS HOW DO YOU DO BAR DIAGRAMS ANDESTIMATE IT WITH PERCENTS